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Mata-Guti\\'errez","submitted_at":"2012-08-03T23:51:38Z","abstract_excerpt":"Let $M(n,\\xi)$ be the moduli space of stable vector bundles of rank $n\\geq 3$ and fixed determinant $\\xi$ over a smooth projective algebraic curve $X$ over $\\mathbb{C}$ of genus $g\\geq 4.$ We use the gonality of the curve and $r$-Hecke morphisms to describe a smooth open set and to compute the dimension of a component of the Hilbert scheme $Hilb_{M(n,\\xi)}$, of the scheme of morphisms $Mor(\\mathbb{G},M(n,\\xi))$ and of the moduli space $ M_{X \\times \\mathbb{G}}$ of stable bundles over $X\\times \\mathbb{G},$ where $\\mathbb{G}$ is the Grassmannian $\\mathbb{G}(n-r,\\mathbb{C}^n)$. 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Brambila-Paz, O. Mata-Guti\\'errez","submitted_at":"2012-08-03T23:51:38Z","abstract_excerpt":"Let $M(n,\\xi)$ be the moduli space of stable vector bundles of rank $n\\geq 3$ and fixed determinant $\\xi$ over a smooth projective algebraic curve $X$ over $\\mathbb{C}$ of genus $g\\geq 4.$ We use the gonality of the curve and $r$-Hecke morphisms to describe a smooth open set and to compute the dimension of a component of the Hilbert scheme $Hilb_{M(n,\\xi)}$, of the scheme of morphisms $Mor(\\mathbb{G},M(n,\\xi))$ and of the moduli space $ M_{X \\times \\mathbb{G}}$ of stable bundles over $X\\times \\mathbb{G},$ where $\\mathbb{G}$ is the Grassmannian $\\mathbb{G}(n-r,\\mathbb{C}^n)$. 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